Probability and Statistics (Check my answer)

In summary, the problem involves a batch of bolts with a mean diameter of 9.711mm and a standard deviation of 0.126mm. The tolerance for this batch is from 9.73mm to 9.97mm. The task is to determine the percentage of bolts rejected assuming they are normally distributed in a batch of 2000 bolts. The correct calculation involves finding the number of standard deviations the tolerance range is from the mean, which is 1.90. This corresponds to an area under the normal curve of 0.9713, meaning that 2.87% of the bolts will be rejected. This translates to 57 rejected bolts out of 2000. However, the given problem may have
  • #1
c00ky
11
0
Hi guys, i was given the following problem:

The mean diameter of a batch of bolts is 9.711mm and the standard deviation of the batch is 0.126mm

The tolerance for this batch of components is 9.73mm to 9.97mm.
In a batch of 2000 bolts, determine the following:

a) The percentage of bolts rejected assuming the bolts are normally distributed.

My answer:

(9.97 - 9.73) / 0.126 = 1.90

1.90 Corresponds to: 0.9713

1 - 0.9713 = 0.0287

(Little less than 3% are rejected)

0.0287 x 2000 = 57.4

= 57 rejected out of 2000

Can anybody tell me if I'm right?
 
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  • #2
No, your first step is not right. But I'm not sure you have written down the problem correctly. If the mean is 9.711, you would expect the tolerated values to go from somewhere below 9.711 to somewhere above it, not from 9.73 to 9.97. Did you mean that the mean is 9.811?
 

1. What is the difference between probability and statistics?

Probability is the study of the likelihood or chance of events occurring, while statistics is the collection, analysis, and interpretation of data.

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Probability is used in everyday life to make decisions, such as choosing the best route to work based on the likelihood of traffic, or determining the chances of winning a game of chance.

3. What is the importance of understanding probability and statistics?

Understanding probability and statistics allows us to make informed decisions based on data and evidence, rather than relying on intuition or guesswork.

4. What are some common misconceptions about probability and statistics?

One common misconception is that a low probability means something is impossible, when in reality it just means it is unlikely. Another is the belief that small sample sizes accurately represent a population.

5. Can probability and statistics be applied to all fields of study?

Yes, probability and statistics are used in a wide range of fields, including medicine, economics, psychology, and engineering, to name a few. These concepts are essential for understanding and analyzing data in any field.

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